Method of determining gnss-ins vehicle attitude based on single antenna

ABSTRACT

The present invention discloses a GNSS-INS vehicle attitude determination method based on a single antenna, including the steps as below: mounting a GNSS antenna at a centroid and in the center of the vehicle, and mounting the IMU measuring unit of the MEMS sensor on the steering shaft of the vehicle; obtaining the position and velocity information of the vehicle by means of the GNSS antenna, obtaining the heading angular speed information of the vehicle by means of the IMU measuring unit; calculating the attitude angle of the vehicle by means of the combination with accelerometer and gyroscope; calculating the heading angle of the vehicle based on the position, velocity, and heading angular speed of the vehicle. The method combines the advantages of the short-term high precision of the IMU gyroscope and the long-term high stability of the GNSS single antenna, so as to avoid the divergence phenomenon.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is the national phase entry of InternationalApplication No. PCT/CN2016/088345, filed on Jul. 04, 2016, which isbased upon and claims priority to Chinese Patent ApplicationNo.201510969458.2 (CN), filed on Dec. 21, 2015, the entire contents ofwhich are incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to an agricultural vehicle automationfiled, particularly relating to a method of determining GNSS-INS vehicleattitude based on a single antenna.

BACKGROUND

With the development of the modern technology and advancements inbiotechnology, GNSS technology, and information technology we see a wideapplication of modern technology in agriculture, leading to theemergence of precision agriculture. As a core carrier of the precisionagriculture, the agricultural machinery automatic driving system issignificant for various agricultural tasks including farming, sowing,fertilization, irrigation, vegetation protection, harvesting, etc.

In order to improve the accuracy of the agricultural vehicle automaticdriving system, it is necessary to measure the navigation accuracies ofagricultural vehicle co-ordinates, the heading angle and the attitudeangle, therefore the measurement values should be as accurate aspossible. In particular, when the agricultural vehicles equipped withGNSS receivers are moving in the fields, the GNSS receiving antenna istilted due to the vibrations of the vehicle body resulting from anuneven force exerted on the tires from the soil. As a result, the GNSSantenna does not coincide with the centroid of the vehicle body, soaccurate attitude angles and heading angles of the vehicle body arenecessary.

At present, the method of measuring GNSS attitudes with multipleantennas is often used. However, this method has the disadvantages ofhigh cost, delay of antenna reception, poor real-time performance anddifficulty in installation. As to the inertial navigation INS used inthe land navigation system for attitude determination, because of highcost etc., it is not applicable to the attitude determination of theagricultural vehicle.

SUMMARY OF THE INVENTION

In view of the above-mentioned deficiencies in the field of agriculturalvehicle automation, the present invention provides a GNSS-INS vehicleattitude determination method based on a single antenna, which canrealize the attitude determination of the vehicle through a singleantenna and improve the accuracy of the attitude determination.

In order to achieve the above objective, an embodiment of the presentinvention employs technical solutions as below:

A GNSS-INS vehicle attitude determination method based on a singleantenna, wherein the GNSS-INS vehicle attitude determination methodbased on a single antenna includes steps as below:

mounting a GNSS antenna at a centroid and in a center of a vehicle, andmounting an IMU measuring unit of a MEMS sensor on a steering shaft ofthe vehicle;

obtaining a position and a velocity of the vehicle by means of the GNSSantenna, obtaining a heading angular speed of the vehicle by means ofthe IMU measuring unit;

calculating an attitude angle of the vehicle by means of a combinationof an accelerometer and a gyroscope;

calculating a heading angle of the vehicle based on the position, thevelocity, and the heading angular speed of the vehicle.

According to one aspect of the present invention, when the IMU measuringunit of the MEMS sensor is fixed on the steering shaft of the vehicle,three axis coordinates of the IUM measuring unit are consistent withthree axis coordinates of the vehicle.

According to one aspect of the present invention, the step ofcalculating the attitude angle of the vehicle by means of thecombination of the accelerometer and the gyroscope comprises:

when a condition that the vehicle is stationary or in a uniform motion,an acceleration of the vehicle is zero, and a rolling angle and a pitchangle of the vehicle are accurately obtained based on a principle of theaccelerometer:

θ = sin⁻¹(a_(x))${\varphi = {\sin^{- 1}\left( \frac{a_{y}}{\cos \; \theta} \right)}},$

wherein a_(x,) a_(y) are accelerations of X axis and Y axis of a carriercoordinate system; θ is the pitch angle; and Ø is the rolling angle;

when the vehicle is running quickly or vibrating seriously, thegyroscope is introduced to calculate the attitude angle by means of thecombination of the accelerometer and the gyroscope, and the specificsteps are as below:

creating a combination filter of the rolling angle and the pitch anglefirst, the combination filter is specifically as below:

$\left\{ {\begin{matrix}{{\overset{.}{x}(t)} = {{{A(t)}{x(t)}} + {w(t)}}} \\{{z(t)} = {{f\left( {x(t)} \right)} + {v(t)}}}\end{matrix},} \right.$

wherein parameters to be estimated are shown as below:

x(t)=[θ φ ω_(x) ω_(y) ω_(z)]^(T),

an observation vector is as below:

z(t)=[^(b) f _(x) ^(b) f _(y) ^(bω) _(ibx) ^(b)ω_(iby) ^(bω)_(ibz)]^(T),

wherein ^(b)f_(x,y) and ^(bω) _(x,y,z) are respective outputs of theaccelerometer and the gyroscope;

a state transition matrix is as below:

${{A(t)} = \begin{bmatrix}0 & 0 & 0 & {\cos \; \varphi} & {{- \sin}\; \varphi} \\0 & 0 & 1 & {\sin \; {\varphi (t)}\tan \; {\theta (t)}} & {\cos \; {\varphi (t)}\tan \; {\theta (t)}} \\0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0\end{bmatrix}},$

an observation design matrix is as below:

f(x(t))=[sin θ cos φ ω_(x) ω_(y) ω_(z)]^(T),

calculating and obtaining the rolling angle and the pitch angle of thevehicle based on above parameters.

According to one aspect of the present invention, the step ofcalculating the attitude angle of the vehicle by means of thecombination of the accelerometer and the gyroscope comprises:

when the vehicle is stationary or in a uniform motion, an accelerationof the vehicle is zero, and the rolling angle and the pitch angle of thevehicle are accurately obtained based on a principle of theaccelerometer:

θ = sin⁻¹(a_(x))${\varphi = {\sin^{- 1}\left( \frac{a_{y}}{\cos \; \theta} \right)}},$

wherein a_(x,) a_(y) are accelerations of X axis and Y axis of a carriercoordinate system; θ is the pitch angle; Ø is the rolling angle;

when the vehicle is running quickly or vibrating seriously, thegyroscope is introduced to calculate the attitude angle by means of thecombination of the accelerometer and the gyroscope, and the specificsteps are as below: since a tilt angle (the rolling angle or the pitchangle) and a tilt angular velocity have a derivative relation, a realtilt angle φ of the system is used as a state vector, a constantdeviation b of the gyroscope is estimated by the accelerometer, and thedeviation b is used as another state vector to obtain a state equationand an observation equation:

$\begin{bmatrix}\overset{.}{\phi} \\\overset{.}{b}\end{bmatrix} = {{\begin{bmatrix}0 & {- 1} \\0 & 0\end{bmatrix}\begin{bmatrix}\phi \\b\end{bmatrix}} + {\begin{bmatrix}1 \\0\end{bmatrix}\omega_{gyro}} + \begin{bmatrix}W_{g} \\0\end{bmatrix}}$ $\phi_{acce} = \left\lbrack {{\begin{matrix}1 & \left. 0 \right\rbrack\end{matrix}\begin{bmatrix}\phi \\b\end{bmatrix}} + W_{a}} \right.$

wherein ω_(gyro) is an angular velocity output by the gyroscope, whereinthe angular velocity includes a fixed deviation, φ_(acce) is an anglevalue processed by the accelerometer, w_(g) is a noise of a measuredvalue from the gyroscope, w_(a) is a noise of a measured value from theaccelerometer, b is a drift error of the gyroscope, w_(g) and w_(a) areindependent from each other, and are both assumed to be white noisesthat satisfy a normal distribution; setting a covariance matrix Q of asystem process noise of the Kalman filter and a covariance matrix R of ameasurement error, formulas of the covariance matrix Q and thecovariance matrix R are as below:

$Q = \begin{bmatrix}{q\_ acce} & 0 \\0 & {q\_ gyro}\end{bmatrix}$ R = [r_acce]

wherein q_acce and q_gyro are respective covariance of the accelerometerand the gyroscope; r_acce is a noise of a measured value from theaccelerometer;

calculating and obtaining the rolling angle and the pitch angle of thevehicle based on above parameters.

According to one aspect of the present invention, the step ofcalculating the heading angle of the vehicle based on the position, thevelocity, and the heading angular speed of the vehicle comprises:

obtaining the heading angle by calculating an eastward velocity and anorthward velocity, a formula of obtaining the heading angle is

ψ_(p)=arctan(v _(E) /v _(N)),

wherein ψ_(p) is the heading angle of the GNSS, v_(E) , v_(N) arerespectively the eastward velocity and the northward velocity;

when the vehicle is stationary or moves at a very low speed, thecombination of a Z axis gyroscope and the GNSS are introduced tocalculate the heading angle accurately, and a system equation and anobservation equation are as below:

$\begin{bmatrix}{\overset{.}{\psi}}_{vel} \\{\overset{.}{b}}_{r}\end{bmatrix} = {{\begin{bmatrix}0 & {- 1} \\0 & {{- 1}/T_{b}}\end{bmatrix}\begin{bmatrix}\psi_{vel} \\b_{r}\end{bmatrix}} + {\begin{bmatrix}1 \\0\end{bmatrix}g_{r}} + {\begin{bmatrix}1 & 0 \\0 & {{- 1}/T_{b}}\end{bmatrix}W_{hd}}}$ $\psi_{GNSS} = \left\lbrack {{\begin{matrix}1 & \left. 0 \right\rbrack\end{matrix}\begin{bmatrix}\psi_{vel} \\g_{bias}\end{bmatrix}} + V_{\psi}} \right.$

wherein, ψ_(GNSS) is the heading angle output by the GNSS, b_(r) is adrift error of the gyroscope, w_(hd) is a noise of a heading process,T_(b) is first-order Markov correlation time;

formulas after linearization are as below:

$\begin{bmatrix}\psi \\b_{r}\end{bmatrix}_{k + 1} = {{{\begin{bmatrix}1 & {- {Ts}} \\0 & 1\end{bmatrix}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k} + {{\begin{bmatrix}T_{s} \\0\end{bmatrix}\left\lbrack r_{m} \right\rbrack}_{k}\lbrack v\rbrack}_{k}} = {H_{yaw}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k}}$

when the vehicle is moving, H_(yaw)=[1 0], otherwise H_(yaw)=[0 0].

According to one aspect of the present invention, the MEMS sensor is asix-axis MEMS sensor.

The advantages of implementing the present invention are provided: AGNSS-INS vehicle attitude determination method based on a single antennaof the present invention, including the steps as below: mounting theGNSS antenna at the centroid and in the center of the vehicle, andmounting the IMU measuring unit of the MEMS sensor on the steering shaftof the vehicle; obtaining the position and velocity information of thevehicle by means of the GNSS antenna, obtaining the heading angularspeed information of the vehicle by means of the IMU measuring unit;calculating the attitude angle of the vehicle by means of a combinationof an accelerometer and a gyroscope; calculating the heading angle ofthe vehicle according to the position, velocity, and heading angularspeed of the vehicle. By means of a combination of the single antennaGNSS and a low cost IMU/MEMS sensor, the attitude and the position canbe determined based on the kinematics model of the agricultural vehicle.The method combines the advantages of the short-term high precision ofthe IMU gyroscope and the long-term high stability of the GNSS singleantenna, so as to avoid the divergence phenomenon which occurs whenusing gyroscope and reduce the noise level of the GNSS attitudedetermination. Hence, the accuracy of the attitude determination can beincreased several times.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The technical solutions in the embodiments of the present invention willbe clearly and fully described with reference to the accompanyingdrawings in the embodiments of the present invention. Obviously, thedescribed embodiments are merely certain embodiments of the inventionand are not intended to be exhaustive. Based on embodiments in thepresent invention, other embodiments obtained by the ordinary personskilled in the art without creative work all fall within the scope ofthe present invention.

Embodiment 1

A GNSS-INS vehicle attitude determination method based on a singleantenna, wherein the GNSS-INS vehicle attitude determination methodbased on a single antenna includes steps as below:

Step S1: mounting the GNSS antenna at the centroid and in the center ofthe vehicle, and mounting the IMU measuring unit of the MEMS sensor onthe steering shaft of the vehicle.

In the step S1, the specific implementation of mounting the GNSS antennaat the centroid and in the center of the vehicle, and mounting the IMUmeasuring unit of the MEMS sensor on the steering shaft of the vehicleis as below: The GNSS antenna is mounted at the centroid and in thecenter of the vehicle to accurately measure the position and velocity ofthe carrier vehicle. When the IMU measuring unit of the MEMS sensor isfixed on the carrier vehicle, the three-axis coordinates of the IMUmeasuring unit are consistent with the three-axis coordinates of thevehicle. At the same time, the IMU measuring unit should be steered inreal-time when the wheel of the vehicle is steered. That is to say, theIMU measuring unit is mounted on the shaft of the vehicle, to make theIMU measuring unit precisely sensitive to the heading angular speed ofthe vehicle, so that sensitive heading information from the IMU isconsistent with the heading information measured from the GNSS.

Step S2: obtaining the position and velocity information of the vehicleby means of a GNSS antenna, and obtaining the heading angular speedinformation of the vehicle by means of the IMU measuring unit.

In the step S2, the position and velocity information of the vehicle areobtained by means of the GNSS antenna, and the heading angular speedinformation of the vehicle is obtained by means of the IMU measuringunit. 3+3 six-axis integrated MEMS-IMU sensor is used to obtain theheading angular rate information of the vehicle accurately.

Step S3: calculating the attitude angle of the vehicle by means of acombination of an accelerometer and a gyroscope.

In the step S3, the attitude angle of the vehicle by means of acombination of the accelerometer and the gyroscope is calculated andspecifically includes the following steps:

Since the measurement accuracy of the gyroscope of the MEMS-IMU is notsensitive to the rotational angular speed of the Earth, so the MEMSsystem cannot be fully self-aligned. When the vehicle is stationary orin a uniform motion, the acceleration of the vehicle is zero, and therolling angle and the pitch angle of the vehicle are accurately obtainedbased on the principle of the accelerometer:

θ = sin⁻¹(a_(x))$\varphi = {{\sin^{- 1}\left( \frac{a_{y}}{\cos \; \theta} \right)}.}$

In the formulas, a_(x,) a_(y) are referred to as the accelerations ofthe x axis and the y axis of the carrier coordinate system; θ isreferred to as the pitch angle; and Ø is referred to as the rollingangle.

When the vehicle is running quickly or vibrating seriously, because ofthe influences of the accelerations from other directions, the attitudeangel cannot be calculated using the above formulas. The gyroscope isthus introduced to perform calculations by means of a combination of theaccelerometer and the gyroscope, and the specific steps are as below:

Creating a combination filter of the rolling angle and the pitch anglefirst, the combination filter is specifically as below:

$\left\{ {\begin{matrix}{{\overset{.}{x}(t)} = {{{A(t)}{x(t)}} + {w(t)}}} \\{{z(t)} = {{f\left( {x(t)} \right)} + {v(t)}}}\end{matrix}.} \right.$

Wherein the parameters to be estimated is as below:

x(t)=[θ φω_(x) ω_(y) ω_(z)]^(T).

The observation vector is as below:

z(t)=[^(b) f _(x) ^(b) f _(y) ^(b)ω_(ibx) ^(b)ω_(iby) ^(b)ω_(ibz)]^(T).

Wherein ^(b)f_(x,y) and ^(b)ω_(ibx,y,z) are respective outputs of theaccelerometer and the gyroscope.

The state transition matrix is as below:

${A(t)} = {\begin{bmatrix}0 & 0 & 0 & {\cos \; \varphi} & {{- \sin}\; \varphi} \\0 & 0 & 1 & {\sin \; {\varphi (t)}\tan \; {\theta (t)}} & {\cos \; {\varphi (t)}\tan \; {\theta (t)}} \\0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0\end{bmatrix}.}$

The observation design matrix is as below:

f(x(t))=[sin θ cos φ ω_(x) ω_(y) ω_(z)]^(T).

Calculating and obtaining the rolling angle and the pitch angle of thevehicle based on the above parameters.

Step S4: calculating the heading angle of the vehicle based on theposition, the velocity, and the heading angular speed of the vehicle.

In the step S4, the heading angle of the vehicle is calculated based onthe position, the velocity and the heading angular speed of the vehicle,and specifically includes: The GNSS attitude determination by the singleantenna mainly uses the GNSS velocity, and the heading angle of vehicleis obtained by calculating the eastward velocity and the northwardvelocity, specifically:

ψ_(p)=arctan(v _(E) /v _(N)).

In the formula, ψ_(p) is referred to as the heading angle of the GNSS,v_(E) , v_(N) are respectively the eastward velocity and the northwardvelocity.

In practical applications, the GNSS heading angle can be extracteddirectly from the NMEA sentences output from the GNSS receiver. However,when the vehicle is stationary or moves at a very low speed, thenumerical values are unstable mathematically, and the velocitymeasurement errors may overwhelm the real velocity values.

In order to improve the heading accuracy, the combination of the Z axisgyroscope and the GNSS are introduced. The gyroscope is mounted alongthe Z axis of the carrier coordinate system. The system equation and theobservation equation are as below:

$\begin{bmatrix}{\overset{.}{\psi}}_{vel} \\{\overset{.}{b}}_{r}\end{bmatrix} = {{\begin{bmatrix}0 & {- 1} \\0 & {{- 1}/T_{b}}\end{bmatrix}\begin{bmatrix}\psi_{vel} \\b_{r}\end{bmatrix}} + {\begin{bmatrix}1 \\0\end{bmatrix}g_{r}} + {\begin{bmatrix}1 & 0 \\0 & {{- 1}/T_{b}}\end{bmatrix}W_{hd}}}$ $\psi_{GNSS} = \left\lbrack {{\begin{matrix}1 & \left. 0 \right\rbrack\end{matrix}\begin{bmatrix}\psi_{vel} \\g_{bias}\end{bmatrix}} + {V_{\psi}.}} \right.$

In the formulas, ψ_(GNSS) is referred to as the heading angle output bythe GNSS, b_(r) is referred to as the drift error of the gyroscope,w_(hd) is referred to as the noise of the heading process, T_(b) isreferred to as the first-order Markov correlation time.

The formulas after linearization are showed as below:

$\begin{bmatrix}\psi \\b_{r}\end{bmatrix}_{k + 1} = {{{\begin{bmatrix}1 & {- {Ts}} \\0 & 1\end{bmatrix}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k} + {{\begin{bmatrix}T_{s} \\0\end{bmatrix}\left\lbrack r_{m} \right\rbrack}_{k}\lbrack v\rbrack}_{k}} = {H_{yaw}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k}}$

When the vehicle is moving, H_(yaw)=[1 0], otherwise H_(yaw)=[0 0].

Finally, the attitude determination of GNSS-INS vehicle based on asingle antenna is realized by calculating the attitude angle of thevehicle and the heading angle.

A GNSS-INS vehicle attitude determination method based on a singleantenna of the present invention, includes the steps as below: mountingthe GNSS antenna at the centroid and in the center of the vehicle, andmounting the IMU measuring unit of the MEMS sensor on the steering shaftof the vehicle; obtaining the position and velocity information of thevehicle by means of the GNSS antenna, and obtaining the heading angularspeed information of the vehicle by means of the IMU measuring unit;calculating the attitude angle of the vehicle by means of a combinationof accelerometer and gyroscope; calculating the heading angle of thevehicle based on the position, velocity, and heading angular speed ofthe vehicle. By means of a combination of the single antenna GNSS andthe IMU/MEMS sensor with a low cost, the attitude and direction aredetermined based on the kinematics model of the agricultural vehicle.The method combines the advantages of the short-term high precision ofthe IMU gyroscope and the long-term high stability of the GNSS singleantenna, so as to avoid the divergence phenomenon which occurs whenusing the gyroscope and reduce the noise level of the GNSS attitudedetermination. Hence, the accuracy of the attitude determination can beincreased several times. An IMU sensor is used in the attitudedetermination method described in the present embodiment, the headingangle error is less than 0.2°, and the pitch angle error and rollingangle error are less than 0.08°. In practical applications, 3+3 six-axisintegrated IMU sensor is used. The 3+3 six-axis integrated IMU sensorhas a small size and light weight, and is cost-effective and modularlydesigned, and thus it can be integrated easily into the agriculturalmachinery auxiliary driving control system.

In practical applications, a tilt sensor can also be used to replace theIMU sensor to achieve the attitude determination solution.

Embodiment 2

A GNSS-INS vehicle attitude determination method based on a singleantenna, wherein the GNSS-INS vehicle attitude determination methodbased on a single antenna includes steps as below:

Step S1: mounting the GNSS antenna at the centroid and in the center ofthe vehicle, and mounting the IMU measuring unit of the MEMS sensor onthe steering shaft of the vehicle.

In the step S1, the specific implementation of mounting the GNSS antennaat the centroid and in the center of the vehicle, and mounting the IMUmeasuring unit of the MEMS sensor on the steering shaft of the vehicleis as below: The GNSS antenna is amounted at the centroid and in thecenter of the vehicle to accurately measure the position and velocity ofthe carrier vehicle. When the IMU measuring unit of the MEMS sensor isfixed on the carrier vehicle, the three-axis coordinates of the IMUmeasuring unit are consistent with the three-axis coordinates of thevehicle. At the same time, the IMU measuring unit should be steered inreal-time when the wheel of the vehicle is steered. That is to say, theIMU measuring unit is mounted on the shaft of the vehicle, to make theIMU measuring unit precisely sensitive to the heading angular speed ofthe vehicle, so that sensitive heading information from the IMU isconsistent with the heading information measured from the GNSS.

Step S2: obtaining the position and velocity information of the vehicleby means of a GNSS antenna, and obtaining the heading angular speedinformation of the vehicle by means of the IMU measuring unit.

In the step S2, the position and velocity information of the vehicle areobtained by means of the GNSS antenna, and the heading angular speedinformation of the vehicle is obtained by means of the IMU measuringunit. 3+3 six-axis integrated MEMS-IMU sensor is used to obtain theheading angular speed information of the vehicle accurately.

Step S3: calculating the attitude angle of the vehicle by means of acombination of an accelerometer and a gyroscope.

In the step S3, the attitude angle of the vehicle by means of acombination of the accelerometer and the gyroscope is calculated andspecifically includes the following steps:

Since the measurement accuracy of the gyroscope of the MEMS-IMU is notsensitive to the rotational angular velocity of the Earth, so the MEMSsystem cannot be fully self-aligned. When the vehicle is stationary orin a uniform motion, the acceleration of the vehicle is zero, and therolling angle and the pitch angle of the vehicle are accurately obtainedbased on the principle of the accelerometer:

θ = sin⁻¹(a_(x))$\varphi = {\sin^{- 1}\left( \frac{a_{y}}{\cos \; \theta} \right)}$

In the formulas, a_(x,) a_(y) are referred to as the accelerations ofthe x axis and the y axis of the carrier coordinate system; θ isreferred to as the pitch angle; and Ø is referred to as the rollingangle.

When the vehicle is running quickly or vibrating seriously, because ofthe influences of the accelerations from other directions, the attitudeangel cannot be calculated using the above formulas. The gyroscope isthus introduced to perform calculations by means of a combination of theaccelerometer and the gyroscope, and the specific steps are as below:

Since the tilt angle (the rolling angle or the pitch angle) and the tiltangular velocity have a derivative relation, the real tilt angle ω ofthe system can be used as a state vector. The constant deviation b ofthe gyroscope is estimated by the accelerometer, and the deviation b isused as another state vector to obtain the corresponding state equationand observation equation:

$\begin{bmatrix}\overset{.}{\phi} \\\overset{.}{b}\end{bmatrix} = {{\begin{bmatrix}0 & {- 1} \\0 & 0\end{bmatrix}\begin{bmatrix}\phi \\b\end{bmatrix}} + {\begin{bmatrix}1 \\0\end{bmatrix}\omega_{gyro}} + \begin{bmatrix}W_{g} \\0\end{bmatrix}}$ $\phi_{acce} = \left\lbrack {{\begin{matrix}1 & \left. 0 \right\rbrack\end{matrix}\begin{bmatrix}\phi \\b\end{bmatrix}} + W_{a}} \right.$

In the formulas, ω_(gyro) is referred to as an angular velocity outputby the gyroscope, wherein the angular velocity includes a fixeddeviation, φ_(acce) is referred to as the angle value processed by theaccelerometer, W_(g) is referred to as the noise of the measurement fromthe gyroscope, W_(a) is referred to as the noise of the measurement fromthe accelerometer, b is referred to as the drift error of the gyroscope,W_(g) and w_(a) are independent from each other, and are both assumed tobe white noise that satisfy the normal distribution. At the same time,the covariance matrix Q of the system process noise of the Kalman filterand the covariance matrix R of the measurement error are set, and theformulas are as below:

$Q = \begin{bmatrix}{q\_ acce} & 0 \\0 & {q\_ gyro}\end{bmatrix}$ R = [r_acce]

In the formulas, the q acce and q gyro are the respective covariance ofthe accelerometer and the gyroscope; r_acce is the noise of themeasurement from the accelerometer.

Calculating and obtaining the rolling angle and the pitch angle of thevehicle based on the above parameters.

Step S4: calculating the heading angle of the vehicle based on theposition, the velocity, and the heading angular speed of the vehicle.

In the step S4, the heading angle of the vehicle is calculated based onthe position, the velocity and the heading angular speed of the vehicle,and specifically includes:

The GNSS attitude determination by the single antenna mainly uses theGNSS velocity, and the heading angle of vehicle is obtained bycalculating the eastward velocity and the northward velocity,specifically:

ψ_(p)=arctan(v _(E) /v _(N)).

In the formula, ψ_(p) is referred to as the heading angle of the GNSS,v_(E) , v_(N) are respectively the eastward velocity and the northwardvelocity.

In practical applications, the GNSS heading angle can be extracteddirectly from the NMEA sentences output from the GNSS receiver. However,when the vehicle is stationary or moves at a very low speed, thenumerical values are unstable mathematically, and the velocitymeasurement errors may overwhelm the real velocity values.

In order to improve the heading accuracy, the combination of the Z axisgyroscope and the GNSS are introduced. The gyroscope is mounted alongthe Z axis of the carrier coordinate system. The system equation and theobservation equation are as below:

$\begin{bmatrix}{\overset{.}{\psi}}_{vel} \\{\overset{.}{b}}_{r}\end{bmatrix} = {{\begin{bmatrix}0 & {- 1} \\0 & {{- 1}/T_{b}}\end{bmatrix}\begin{bmatrix}\psi_{vel} \\b_{r}\end{bmatrix}} + {\begin{bmatrix}1 \\0\end{bmatrix}g_{r}} + {\begin{bmatrix}1 & 0 \\0 & {{- 1}/T_{b}}\end{bmatrix}W_{hd}}}$ $\psi_{GNSS} = \left\lbrack {{\begin{matrix}1 & \left. 0 \right\rbrack\end{matrix}\begin{bmatrix}\psi_{vel} \\g_{bias}\end{bmatrix}} + V_{\psi}} \right.$

In the formulas, ψ_(GNSS) is referred to as the heading angle output bythe GNSS, b_(r) is referred to as the drift error of the gyroscope,w_(hd) is referred to as the noise of the heading process, T_(b) isreferred to as the first-order Markov correlation time.

The formulas after linearization are shown below:

$\begin{bmatrix}\psi \\b_{r}\end{bmatrix}_{k + 1} = {{{\begin{bmatrix}1 & {- {Ts}} \\0 & 1\end{bmatrix}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k} + {{\begin{bmatrix}T_{s} \\0\end{bmatrix}\left\lbrack r_{m} \right\rbrack}_{k}\lbrack v\rbrack}_{k}} = {H_{yaw}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k}}$

When the vehicle is moving, H_(yaw)=[1 0], otherwise H_(yaw)=[0 0].

Finally, the attitude determination of GNSS-INS vehicle based on asingle antenna is realized by calculating the attitude angle of thevehicle and the heading angle.

A GNSS-INS vehicle attitude determination method based on a singleantenna of the present invention, includes the steps as below: mountingthe GNSS antenna at the centroid and in the center of the vehicle, andmounting the IMU measuring unit of the MEMS sensor on the steering shaftof the vehicle; obtaining the position and velocity information of thevehicle by means of the GNSS antenna, and obtaining the heading angularspeed information of the vehicle by means of the IMU measuring unit;calculating the attitude angle of the vehicle by means of a combinationof accelerometer and gyroscope; calculating the heading angle of thevehicle based on the position, velocity, and heading angular speed ofthe vehicle. By means of a combination of the single antenna GNSS andthe IMU/MEMS sensor with a low cost, the attitude and direction aredetermined based on the kinematics model of the agricultural vehicle.The method combines the advantages of the short-term high precision ofthe IMU gyroscope and the long-term high stability of the GNSS singleantenna, so as to avoid the divergence phenomenon which occurs whenusing gyroscope and reduce the noise level of the GNSS attitudedetermination. Hence, the accuracy of the attitude determination can beincreased several times. An IMU sensor is used in the attitudedetermination method described in the present embodiment, the headingangle error is less than 0.2°, and the pitch angle error and rollingangle error are less than 0.08°. In practical applications, 3+3 six-axisintegrated IMU sensor is used. The 3+3 six-axis integrated IMU sensorhas a small size and light weight, and is cost-effective and modularlydesigned, and thus it can be integrated easily into the agriculturalmachinery auxiliary driving control system.

In practical applications, a tilt sensor can also be used to replace theIMU sensor to achieve the attitude determination solution.

The description above is only related to the specific embodiments of thepresent invention, but is not intended to limit the scope of the presentinvention. Various modifications or replacements within the scope of thepresent invention, which can be easily conceived by the ordinary personskilled in the art, should fall within the scope of the presentinvention. Therefore, the scope of the present invention should bedetermined by the scope of the claims.

What is claimed is:
 1. A method of determining GNSS-INS vehicle attitudebased on a single antenna, wherein the method comprising: mounting aGNSS antenna at a centroid and in a center of a vehicle, and mounting anIMU measuring unit of a MEMS sensor on a steering shaft of the vehicle;obtaining a position and a velocity of the vehicle by means of the GNSSantenna, obtaining a heading angular speed of the vehicle by means ofthe IMU measuring unit; calculating an attitude angle of the vehicle bymeans of a combination of an accelerometer and a gyroscope; calculatinga heading angle of the vehicle based on the position, the velocity, andthe heading angular speed of the vehicle.
 2. The method of determiningGNSS-INS vehicle attitude based on a single antenna of claim 1, whereinwhen the IMU measuring unit of the MEMS sensor is fixed on the steeringshaft of the vehicle, three axis coordinates of the IUM measuring unitare consistent with three axis coordinates of the vehicle.
 3. The methodof determining GNSS-INS vehicle attitude based on a single antenna ofclaim 1, wherein the step of calculating the attitude angle of thevehicle by means of the combination of the accelerometer and thegyroscope comprises: when a condition that the vehicle is stationary orin a uniform motion, an acceleration of the vehicle is zero, and arolling angle and a pitch angle of the vehicle are accurately obtainedbased on a principle of the accelerometer: θ = sin⁻¹(a_(x))${\varphi = {\sin^{- 1}\left( \frac{a_{y}}{\cos \; \theta} \right)}},$wherein a_(x,) a_(y) are accelerations of X axis and Y axis of a carriercoordinate system; θ is the pitch angle; and Ø is the rolling angle;when the vehicle is running quickly or vibrating seriously, thegyroscope is introduced to calculate the attitude angle by means of thecombination of the accelerometer and the gyroscope, and the specificsteps are as below: creating a combination filter of the rolling angleand the pitch angle first, the combination filter is specifically asbelow: $\left\{ {\begin{matrix}{{\overset{.}{x}(t)} = {{{A(t)}{x(t)}} + {w(t)}}} \\{{z(t)} = {{f\left( {x(t)} \right)} + {v(t)}}}\end{matrix},} \right.$ wherein parameters to be estimated are shown asbelow:x(t)=[θ φ ω_(x) ω_(y) ω_(z)]^(T), an observation vector is as below:z(t)=[^(b) f _(x) ^(b) f _(y) ^(b)ω_(ibx) ^(b)ω_(iby) ^(bω) _(ibz)]^(T),wherein ^(b)f_(x,y) and ^(b)ω_(ibx,y,z) are respective outputs of theaccelerometer and the gyroscope; a state transition matrix is as below:${{A(t)} = \begin{bmatrix}0 & 0 & 0 & {\cos \; \varphi} & {{- \sin}\; \varphi} \\0 & 0 & 1 & {\sin \; {\varphi (t)}\tan \; {\theta (t)}} & {\cos \; {\varphi (t)}\; \tan \; {\theta (t)}} \\0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0\end{bmatrix}},$ an observation design matrix is as below:f(x(t))=[sin θ cos φ ω_(x) ω_(y) ω_(z)]^(T), calculating and obtainingthe rolling angle and the pitch angle of the vehicle based on aboveparameters.
 4. The method of determining GNSS-INS vehicle attitude basedon a single antenna of claim 1, wherein the step of calculating theattitude angle of the vehicle by means of the combination of theaccelerometer and the gyroscope comprises: when the vehicle isstationary or in a uniform motion, an acceleration of the vehicle iszero, and the rolling angle and the pitch angle of the vehicle areaccurately obtained based on a principle of the accelerometer:θ = sin⁻¹(a_(x))${\varphi = {\sin^{- 1}\left( \frac{a_{y}}{\cos \; \theta} \right)}},$wherein a_(x,) a_(y) are accelerations of X axis and Y axis of a carriercoordinate system; θ is the pitch angle; Ø is the rolling angle; whenthe vehicle is running quickly or vibrating seriously, the gyroscope isintroduced to calculate the attitude angle by means of the combinationof the accelerometer and the gyroscope, and the specific steps are asbelow: since a tilt angle and a tilt angular velocity have a derivativerelation, a real tilt angle φ of the system is used as a state vector, aconstant deviation b of the gyroscope is estimated by the accelerometer,and the deviation b is used as another state vector to obtain a stateequation and an observation equation: $\begin{bmatrix}\overset{.}{\phi} \\\overset{.}{b}\end{bmatrix} = {{\begin{bmatrix}0 & {- 1} \\0 & 0\end{bmatrix}\begin{bmatrix}\phi \\b\end{bmatrix}} + {\begin{bmatrix}1 \\0\end{bmatrix}\omega_{gyro}} + \begin{bmatrix}w_{g} \\0\end{bmatrix}}$ $\phi_{acce} = {{\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix}\phi \\b\end{bmatrix}} + w_{a}}$ wherein ω_(gyro) is an angular velocity outputby the gyroscope, wherein the angular velocity includes a fixeddeviation, φ_(acce) is an angle value processed by the accelerometer,w_(g) is a noise of a measured value from the gyroscope, w_(a) is anoise of a measured value from the accelerometer, b is a drift error ofthe gyroscope, w_(g) and w_(a) are independent from each other, and areboth assumed to be white noises that satisfy a normal distribution;setting a covariance matrix Q of a system process noise of the Kalmanfilter and a covariance matrix R of a measurement error, formulas of thecovariance matrix Q and the covariance matrix R are as below:$Q = {{\begin{bmatrix}{q\_ acce} & 0 \\0 & {q\_ gyro}\end{bmatrix}\mspace{31mu} R} = \lbrack{r\_ acce}\rbrack}$ whereinq_acce and q_gyro are respective covariance of the accelerometer and thegyroscope; r_acce is a noise of a measured value from the accelerometer;calculating and obtaining the rolling angle and the pitch angle of thevehicle based on above parameters.
 5. The method of determining GNSS-INSvehicle attitude based on a single antenna according to claim 1, whereinthe step of calculating the heading angle of the vehicle based on theposition, the velocity, and the heading angular speed of the vehiclecomprises: obtaining the heading angle by calculating an eastwardvelocity and a northward velocity, a formula of obtaining the headingangle isψ_(P)=arctan(v _(E) /v _(N)), wherein ψ_(p) is the heading angle of theGNSS, v_(E) , v_(N) are respectively the eastward velocity and thenorthward velocity; when the vehicle is stationary or moves at a verylow speed, the combination of a Z axis gyroscope and the GNSS areintroduced to calculate the heading angle accurately, and a systemequation and an observation equation are as below: $\begin{bmatrix}{\overset{.}{\psi}}_{vel} \\{\overset{.}{b}}_{r}\end{bmatrix} = {{\begin{bmatrix}0 & {- 1} \\0 & {{- 1}/T_{b}}\end{bmatrix}\begin{bmatrix}\psi_{vel} \\b_{r}\end{bmatrix}} + {\begin{bmatrix}1 \\0\end{bmatrix}g_{r}} + {\begin{bmatrix}1 & 0 \\0 & {{- 1}/T_{b}}\end{bmatrix}w_{hd}}}$ $\psi_{GNSS} = {{\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix}\psi_{vel} \\g_{bias}\end{bmatrix}} + v_{\psi}}$ wherein, ψ_(GNSS) is the heading angleoutput by the GNSS, b_(r) is a drift error of the gyroscope, w_(hd) is anoise of a heading process, T_(b) is first-order Markov correlationtime; formulas after linearization are as below: $\begin{bmatrix}\psi \\b_{r}\end{bmatrix}_{k + 1} = {{{\begin{bmatrix}1 & {- {Ts}} \\0 & 1\end{bmatrix}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k} + {{\begin{bmatrix}T_{s} \\0\end{bmatrix}\left\lbrack r_{m} \right\rbrack}_{k}\lbrack v\rbrack}_{k}} = {H_{yaw}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k}}$ when the vehicle is moving, H_(yaw)=[1 0],otherwise H_(yaw)=[0 0].
 6. The method of determining GNSS-INS vehicleattitude based on a single antenna of claim 5, wherein the MEMS sensoris a six-axis MEMS sensor.
 7. The method of determining GNSS-INS vehicleattitude based on a single antenna according to claim 2, wherein thestep of calculating the heading angle of the vehicle based on theposition, the velocity, and the heading angular speed of the vehiclecomprises: obtaining the heading angle by calculating an eastwardvelocity and a northward velocity, a formula of obtaining the headingangle isψ_(P)=arctan(v _(E) /v _(N)), wherein ψ_(p) is the heading angle of theGNSS, v_(E) , v_(N) are respectively the eastward velocity and thenorthward velocity; when the vehicle is stationary or moves at a verylow speed, the combination of a Z axis gyroscope and the GNSS areintroduced to calculate the heading angle accurately, and a systemequation and an observation equation are as below: $\begin{bmatrix}{\overset{.}{\psi}}_{vel} \\{\overset{.}{b}}_{r}\end{bmatrix} = {{\begin{bmatrix}0 & {- 1} \\0 & {{- 1}/T_{b}}\end{bmatrix}\begin{bmatrix}\psi_{vel} \\b_{r}\end{bmatrix}} + {\begin{bmatrix}1 \\0\end{bmatrix}g_{r}} + {\begin{bmatrix}1 & 0 \\0 & {{- 1}/T_{b}}\end{bmatrix}w_{hd}}}$ $\psi_{GNSS} = {{\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix}\psi_{vel} \\g_{bias}\end{bmatrix}} + v_{\psi}}$ wherein, V_(GNSS) is the heading angleoutput by the GNSS, b_(r) is a drift error of the gyroscope, w_(hd) is anoise of a heading process, T_(b) is first-order Markov correlationtime; formulas after linearization are as below: $\begin{bmatrix}\psi \\b_{r}\end{bmatrix}_{k + 1} = {{{\begin{bmatrix}1 & {- {Ts}} \\0 & 1\end{bmatrix}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k} + {{\begin{bmatrix}T_{s} \\0\end{bmatrix}\left\lbrack r_{m} \right\rbrack}_{k}\lbrack v\rbrack}_{k}} = {H_{yaw}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k}}$ when the vehicle is moving, H_(yaw)=[1 0],otherwise H_(yaw)=[0 0].
 8. The method of determining GNSS-INS vehicleattitude based on a single antenna according to claim 3, wherein thestep of calculating the heading angle of the vehicle based on theposition, the velocity, and the heading angular speed of the vehiclecomprises: obtaining the heading angle by calculating an eastwardvelocity and a northward velocity, a formula of obtaining the headingangle isψ_(p)=arctan(v _(E) /v _(N)) wherein ψ_(p) is the heading angle of theGNSS, v_(E) , v_(N) are respectively the eastward velocity and thenorthward velocity; when the vehicle is stationary or moves at a verylow speed, the combination of a Z axis gyroscope and the GNSS areintroduced to calculate the heading angle accurately, and a systemequation and an observation equation are as below: $\begin{bmatrix}{\overset{.}{\psi}}_{vel} \\{\overset{.}{b}}_{r}\end{bmatrix} = {{\begin{bmatrix}0 & {- 1} \\0 & {{- 1}/T_{b}}\end{bmatrix}\begin{bmatrix}\psi_{vel} \\b_{r}\end{bmatrix}} + {\begin{bmatrix}1 \\0\end{bmatrix}g_{r}} + {\begin{bmatrix}1 & 0 \\0 & {{- 1}/T_{b}}\end{bmatrix}w_{hd}}}$ $\psi_{GNSS} = {{\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix}\psi_{vel} \\g_{bias}\end{bmatrix}} + v_{\psi}}$ wherein, ψ_(GNSS) is the heading angleoutput by the GNSS, b_(r) is a drift error of the gyroscope, w_(hd) is anoise of a heading process, T_(b) is first-order Markov correlationtime; formulas after linearization are as below: $\begin{bmatrix}\psi \\b_{r}\end{bmatrix}_{k + 1} = {{{\begin{bmatrix}1 & {- {Ts}} \\0 & 1\end{bmatrix}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k} + {{\begin{bmatrix}T_{s} \\0\end{bmatrix}\left\lbrack r_{m} \right\rbrack}_{k}\lbrack v\rbrack}_{k}} = {H_{yaw}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k}}$ when the vehicle is moving, H_(yaw)=[1 0],otherwise H_(yaw)=[0 0].
 9. The method of determining GNSS-INS vehicleattitude based on a single antenna according to claim 4, wherein thestep of calculating the heading angle of the vehicle based on theposition, the velocity, and the heading angular speed of the vehiclecomprises: obtaining the heading angle by calculating an eastwardvelocity and a northward velocity, a formula of obtaining the headingangle isψ_(p)=arctan(v _(E) /v _(N)) wherein ψ_(p) is the heading angle of theGNSS, v_(E) , v_(N) are respectively the eastward velocity and thenorthward velocity; when the vehicle is stationary or moves at a verylow speed, the combination of a Z axis gyroscope and the GNSS areintroduced to calculate the heading angle accurately, and a systemequation and an observation equation are as below: $\begin{bmatrix}{\overset{.}{\psi}}_{vel} \\{\overset{.}{b}}_{r}\end{bmatrix} = {{\begin{bmatrix}0 & {- 1} \\0 & {{- 1}/T_{b}}\end{bmatrix}\begin{bmatrix}\psi_{vel} \\b_{r}\end{bmatrix}} + {\begin{bmatrix}1 \\0\end{bmatrix}g_{r}} + {\begin{bmatrix}1 & 0 \\0 & {{- 1}/T_{b}}\end{bmatrix}w_{hd}}}$ $\psi_{GNSS} = {{\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix}\psi_{vel} \\g_{bias}\end{bmatrix}} + v_{\psi}}$ wherein, ψ_(GNSS) is the heading angleoutput by the GNSS, b_(r) is a drift error of the gyroscope, w_(hd) is anoise of a heading process, T_(b) is first-order Markov correlationtime; formulas after linearization are as below: $\begin{bmatrix}\psi \\b_{r}\end{bmatrix}_{k + 1} = {{{\begin{bmatrix}1 & {- {Ts}} \\0 & 1\end{bmatrix}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k} + {{\begin{bmatrix}T_{s} \\0\end{bmatrix}\left\lbrack r_{m} \right\rbrack}_{k}\lbrack v\rbrack}_{k}} = {H_{yaw}\begin{bmatrix}\hat{\psi} \\{\hat{b}}_{r}\end{bmatrix}}_{k}}$ when the vehicle is moving, H_(yaw)=[1 0],otherwise H_(yaw)=[0 0].
 10. The method of determining GNSS-INS vehicleattitude based on a single antenna of claim 7, wherein the MEMS sensoris a six-axis MEMS sensor.
 11. The method of determining GNSS-INSvehicle attitude based on a single antenna of claim 8, wherein the MEMSsensor is a six-axis MEMS sensor.
 12. The method of determining GNSS-INSvehicle attitude based on a single antenna of claim 9, wherein the MEMSsensor is a six-axis MEMS sensor.